Symmetry-Breaking and Hysteresis in a Duplex Voter Model
Adaptation and Self-Organizing Systems
2026-04-08 v1 Dynamical Systems
Physics and Society
Abstract
We introduce and analyze a voter-type model on a two-layer multiplex network, where the presence of a state on one layer acts as a catalyst or inhibitor to the propagation of that state on the other layer. Despite the model's simplicity, our mathematical analysis reveals a rich phase diagram that includes spontaneous symmetry-breaking and a cusp bifurcation, which arises when noise is introduced into the model. In particular, this bifurcation mechanism can be viewed as a prototypical unfolding of the change between explosive and non-explosive transitions observed in various other network models. We cross-validate our analytic results by numerical simulations.
Keywords
Cite
@article{arxiv.2604.05860,
title = {Symmetry-Breaking and Hysteresis in a Duplex Voter Model},
author = {Christian Kluge and Christian Kuehn},
journal= {arXiv preprint arXiv:2604.05860},
year = {2026}
}